Write a formula for f(t) as a sum of Heaviside functions. Type uc for the Heaviside function that jumps at c (don't type uc(t) ). F(t) = t, 0 ≤ t ≤ 3 2t−3, 3 < t ≤ 4 5, 4 < t

Answer: The weight of the Apples is 160g

Step-by-step explanation:

If the apples were priced at $3.50/kg, then the cost of 1 kg of apples would be $3.50.

To find out the weight of 12 apples, we can divide the total cost of $6.72 by the cost of 1 kg of apples:

$6.72 ÷ $3.50/kg = 1.92 kg

So, the weight of 12 apples is 1.92 kg.

To find the average weight of 1 apple, we can divide the total weight of the 12 apples by the number of apples:

1.92 kg ÷ 12 = 0.16 kg

Finally, we need to convert the weight of 1 apple from kilograms to grams:

0.16 kg x 1000 g/kg = 160 g

Therefore, the average weight of an apple in grams is 160 g.

For accounting purposes, depreciation is an allocation of a cost of an asset.

Both depreciation and amortization are techniques for spreading out an asset's cost throughout its useful life, although they are employed for various asset categories. Whereas amortisation is used for intangible assets like patents, copyrights, and trademarks, depreciation is utilised for tangible assets like buildings, machinery, and equipment. Depreciation is a method used to account for an asset's decline in value as a result of damage or obsolescence. During the course of the asset's useful life, the asset's cost is distributed to match the income it produces.

Depreciation is an accounting technique used to distribute a tangible asset's cost over the course of its useful life.

Hence, for accounting purposes, depreciation is an allocation of a cost of an asset.

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Answer:

B. Isosceles right triangle

C. Quadrilateral

D. Parallelogram

Step-by-step explanation:

Answer:

The geometric figures that could describe how the garden might look are B. Isosceles right triangle and C. Quadrilateral.

Answer:

( 9, 1/7 )

Step-by-step explanation:

I/9x- y=6/7                  equation    (1)

1/18x-2y=3/14              equation    (2)

9x(1)-18x(2)              multiply equation (1 ) by 9 and (2 ) by 18 and subtract  

                                                                                                      them                                                                                                                

we get y=1/7

then put the value of y=1/7 in ( 1 ) or (2)

1/9x-1/7=6/7 ⇒x=9

therefore  the right answer is ( 9, 1/7 )

Answer:

 16/99

Step-by-step explanation:

so you turn into an algebraic equation

[tex]x[/tex] = 0.1616161616

100[tex]x[/tex]=16.161616

100[tex]x[/tex]-1[tex]x[/tex]=99[tex]x[/tex]

99[tex]x[/tex]=16.1616-0.1616

     = 16

[tex]x[/tex]= [tex]\frac{16}{99}[/tex]

Answer:

2x - 13

Step-by-step explanation:

If x represents the greater number, then the other number is x - 13. The sum of these two numbers is:

x + (x - 13) = 2x - 13

To estimate the distance traveled  we need to find the area under the velocity-time graph from 0 to 8 seconds So,The estimate for the distance the car traveled for the first 8 seconds is 4000 meters.

A velocity-time graph is a graphical representation that shows the velocity of an object on the y-axis and time on the x-axis. It is used to depict the change in velocity over time and can provide information about the acceleration or deceleration of an object.

The height of each strip can be estimated by taking the average of the velocities at the beginning and end of the strip.

Using the trapezium rule, the estimated area of each strip is:

Strip 1: 0.5 x (0 + 2) x (0 + (-500)) = -500 m/s

Strip 2: 0.5 x (2 + 4) x (-500 + (-1000)) = -1500 m/s

Strip 3: 0.5 x (4 + 6) x (-1000 + (-500)) = -1500 m/s

Strip 4: 0.5 x (6 + 8) x (-500 + 0) = -500 m/s

The total estimated area is the sum of the areas of the 4 strips:

Total estimated area = -500 + (-1500) + (-1500) + (-500) = -4000 m/s

Since the area represents the distance traveled by the car, we can take the absolute value of the area to get the estimated distance traveled:

Estimated distance traveled is = |-4000| = 4000 meters

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Yes, it is possible to write 7 as a linear combination of the given vectors V1, V2, and V3 with coefficients that are not all zero.

One such linear combination can be given as follows:7 = -3V1 + 4V2 + V3To prove that this is indeed a linear combination of the given vectors, we can substitute the given vectors and coefficients in the above expression and verify that it gives the desired result.

So, we have:RHS = -3V1 + 4V2 + V3= -3(2i - 3j + k) + 4(-i + 2j + 3k) + (i - j - k)= -6i + 9j - 3k - i + 8j + 12k + i - j - k= 7j + 8kSince this result matches with the given vector 7, we can conclude that 7 can be written as a linear combination of the given vectors with coefficients that are not all zero.Hence, the required linear combination is:7 = -3V1 + 4V2 + V3.

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Anna should use 10 mL of the 72% salt solution and 20 mL of the 54% salt solution to make 30 mL of a 60% salt solution

Let's assume that Anna will use x mL of the 72% salt solution, and therefore she will use (30 - x) mL of the 54% salt solution (since the total volume is 30 mL).

To find out how much of each solution Anna should use, we can set up an equation based on the amount of salt in each solution.

The amount of salt in x mL of 72% salt solution is

= 0.72x

The amount of salt in (30 - x) mL of 54% salt solution is

= 0.54(30 - x)

To make a 60% salt solution, the total amount of salt in the final solution should be

0.6(30) = 18

So we can set up an equation

0.72x + 0.54(30 - x) = 1

Simplifying the equation

0.72x + 16.2 - 0.54x = 18

0.18x = 1.8

x = 10 ml

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Answer:

- 1 and 7

Step-by-step explanation:

to find h(0) substitute x = 0 into h(x)

h(0) = 4(0) - 1 = 0 - 1 = - 1

to find h2) substitute x = 2 into h(x)

h(2) = 4(2) - 1 = 8 - 1 = 7

Answer:

Step-by-step explanation:

Let's say Jeff ordered x tacos and y burritos.

From the problem, we know that:

- The calorie count of one taco is 150 calories

- The calorie count of one burrito is 380 calories

- Jeff ordered a total of 11 items

- Jeff consumed a total of 3030 calories

We can use the information given to form a system of equations:

x + y = 11 (Jeff ordered a total of 11 items)

150x + 380y = 3030 (Jeff consumed a total of 3030 calories)

To solve this system, we can use substitution.

Rearranging the first equation, we get:

x = 11 - y

Substituting this value of x into the second equation, we get:

150(11 - y) + 380y = 3030

Expanding and simplifying:

1650 - 150y + 380y = 3030

230y = 1380

y = 6

So Jeff ordered 6 burritos.

Substituting this value of y back into the first equation, we get:

x + 6 = 11

x = 5

So Jeff ordered 5 tacos.

Therefore, Jeff ordered 5 tacos and 6 burritos.

The quadratic form are a) ′ = ᵢⱼ∑ ᵢⱼᵢ, b)  ′()=′, c) ((+)/2)=′, d) 2−3²−².
The question is asking for an expression of the quadratic form with coefficient matrix A for 2c-3rjt2-z2.
For (a): The quadratic form of the vector x with coefficient matrix A is expressed as ′ = ᵢⱼ∑ ᵢⱼᵢ, where is an × matrix and is an -vector.
For (b): Taking the transpose of the triple product ′ we get ′()=′, which shows that the quadratic form with the transposed coefficient matrix has the same value for any a.
For (c): The quadratic form with coefficient matrix equal to the symmetric part of a matrix (i.e., (A+AT)/2) is expressed as ((+)/2)=′, which shows that the quadratic form with coefficient matrix equal to the symmetric part of a matrix has the same value as the original quadratic form.
For (d): The expression 2c-3rjt2-z2 as a quadratic form, with symmetric coefficient matrix A, is expressed as ((+)/2)= 2−3²−², where is a symmetric matrix.

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Answer:

[tex]\large\boxed{\textsf{The Original Number is 13.}}[/tex]

Step-by-step explanation:

[tex]\textsf{We are asked to identify the original number.}[/tex]

[tex]\textsf{Many changes have happened to the original number that it is 9.}[/tex]

[tex]\textsf{We can identify the original number by using the Inverse Operation.}[/tex]

[tex]\large\underline{\textsf{What are Inverse Operations?}}[/tex]

[tex]\textsf{Inverse Operations are like normal operations, but they are reverse.}[/tex]

[tex]\mathtt{(+ , -, \times, \div)}[/tex]

[tex]\large\underline{\textsf{For Example;}}[/tex]

[tex]\textsf{The Inverse Operation of Addition is Subtraction.}[/tex]

[tex]\textsf{The Inverse Operation of Division is Multiplication.}[/tex]

[tex]\textsf{Basically, we will work backwards to find the original number.}[/tex]

[tex]\large\underline{\textsf{Solve;}}[/tex]

[tex]\textsf{Let's start with 9.}[/tex]

[tex]\mathtt{9 \times 5 = 45.} \ \textsf{(The Inverse Operation is Multiplication.)}[/tex]

[tex]\mathtt{45-10=35} \ \textsf{(The Inverse Operation is Subtraction.)}[/tex]

[tex]\mathtt{35 \div 7 = 5} \ \textsf{(The Inverse Operation is Division.)}[/tex]

[tex]\mathtt{5+8=13} \ \textsf{(The Inverse Operation is Addition.)}[/tex]

[tex]\large\boxed{\textsf{The Original Number is 13.}}[/tex]

Answer:

2=x y=-6

Step-by-step explanation:

x+y=-4

x-y=8

(-)(-)=+

(-)(+)=-

2+-6=-4

2--6=8

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Answer: 3.2.1. Money, goods, services, and factors of production flow between Jacob's Pet Shop, consumers, and the government as follows:

Money flows from consumers to Jacob's Pet Shop when they purchase pet food and accessories, and from Jacob's Pet Shop to the government in the form of taxes.

Goods and services flow from Jacob's Pet Shop to consumers when they purchase pet food and accessories, and from the government to Jacob's Pet Shop in the form of contracts or grants for the delivery service.

Factors of production flow from Jacob's Pet Shop to the economy in the form of employment opportunities for the shop manager, shop assistants, and driver, and from the economy to Jacob's Pet Shop in the form of raw materials and supplies for the business.

3.2.2. The diagram below illustrates the flow of money, goods and services, and factors of production between Jacob's Pet Shop, consumers, and the government:

               +--------------------+

               |                    |

               |     Consumers      |

               |                    |

               +--------+-----------+

                        | Purchase pet food and accessories

               +--------v-----------+

               |                      |

               | Jacob's Pet Shop     |

               |                      |

               +-------+--------------+

                       | Sell pet food and accessories

                       |

             +---------v-----------+

             |                     |

             |      Government      |

             |                     |

             +---------------------+

3.3. Two features that a closed economy will prohibit are:

International trade: A closed economy does not engage in trade with other countries. All economic activity is confined within the borders of the country.

Movement of capital: A closed economy does not allow the free movement of capital, such as investments or loans, in and out of the country. All capital transactions are restricted within the economy.

was this worth 5 points no way.

Step-by-step explanation:

Answer: To plot and connect the points, you can use a graphing software or a graphing calculator. Once the points are plotted, you can determine if the graph is linear or exponential by looking at the slope of the line. If the slope is increasing or decreasing exponentially, the graph is exponential. If the slope is constant, the graph is linear.

Step-by-step explanation:

By using the formula of a geometric sequence, the 14th term will be 125/1024

We have, the Fourth term of geometric sequence T_4= 125 and T_10 = 125/64

Let's find the first term and common ratio of the geometric sequence.

Using the formula of the nth term of a geometric sequence, we get,

T_4 = a * r^3 = 125 ....(1)

and,

T_10 = a * r^9 = 125/64 ...(2)

On dividing eq. (2) by eq. (1), we get,

(r^6) = (125/64) / 125 ⇒ 1/64

Taking the sixth root of both sides, we get:

r = (1/64)^(1/6)

r = 1/2

Now that we know the common ratio, we can use the equation for the nth term of a geometric sequence:

T_n = a * r^(n-1)

To find the 14th term, we substitute n=14 and solve:

T_14 = a * (1/2)^(14-1) ⇒ a * (1/2)^13

We don't know the value of a yet, but we can use the fact that the 4th term is 125 to solve for it:

a * r^3 = 125

a * (1/2)^3 = 125

a = 125 * 2^3

a = 1000

Substituting this value for a, we get:

T_14 = 1000 * (1/2)^13

T_14 = 1000 * 1/8192

T_14= 125/1024

Therefore, the 14th term of the geometric sequence is 125/1024.

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We are interested in the population proportion of drivers who claim they always buckle upa.i. x = 320 ii. n = 400 iii. p′ = 0.8

b. The random variable X represents the number of drivers out of the sample of 400 who claim they always buckle up, while P′ represents the sample proportion of drivers who claim they always buckle up.

c. The distribution to use for this problem is the normal distribution because the sample size is large enough (n=400) and the population proportion is not known.

d. i. The 95% confidence interval for the population proportion who claim they always buckle up is (0.7709, 0.8291).

ii. The graph is a normal distribution curve with mean p′ = 0.8 and standard deviation σ = sqrt[p′(1-p′)/n].

iii. The error bound is 0.0291.

e. Three difficulties the insurance companies might have in obtaining random results from a telephone survey are:

Selection bias: The survey might not be truly random if the telephone numbers selected are not representative of the population of interest.

Nonresponse bias: People may choose not to participate in the survey or may not be reached, which could bias the results.

Social desirability bias: Respondents may give socially desirable answers rather than their true opinions, which could also bias the results.

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Answer: $15.25

Step-by-step explanation:

Let x be the number of apples purchased and y be the number of mangos purchased. Then we have the following constraints:

2.25x + 1.25y ≤ 20 (Jose has $20 to spend)

x + y ≥ 9 (Jose must buy at least 9 apples and mangos altogether)

x ≥ 3 (Jose must buy at least 3 apples)

y ≤ 9 (Jose can buy at most 9 mangos)

To solve this system of inequalities graphically, we can plot the relevant lines and shade the feasible region.

First, we graph the line 2.25x + 1.25y = 20 by finding its intercepts:

When x = 0, we have 1.25y = 20, so y = 16.

When y = 0, we have 2.25x = 20, so x = 8.89 (rounded to two decimal places).

Plotting these intercepts and connecting them with a line, we get:

     |       *

 16  |   *    

     |      

     |  /    

     | /      

     |/      

 0   *--------*

      0    8.89

Next, we graph the line x + y = 9 by finding its intercepts:

When x = 0, we have y = 9.

When y = 0, we have x = 9.

Plotting these intercepts and connecting them with a line, we get:

    |      

 9   |   *    

     |      

     |  /    

     | /      

     |/      

 0   *--------*

      0    9  

Finally, we shade the feasible region by considering the remaining constraints:

x ≥ 3: This means we shade to the right of the line x = 3.

y ≤ 9: This means we shade below the line y = 9.

Shading these regions and finding their intersection, we get:

   |       *

 16  |   *    |

     |       |

     |  /    |

     | /     |

     |/      |

 9   *--------*---

     |       | /

     |       |/

     |       *

 0   *--------*

      3    8.89

The feasible region is the shaded triangle bounded by the lines 2.25x + 1.25y = 20, x + y = 9, and x = 3.

To find one possible solution, we can pick any point within the feasible region. For example, the point (4, 5) satisfies all the constraints and represents buying 4 apples and 5 mangos, which costs 4(2.25) + 5(1.25) = $15.25.

As a result, segment AE's length matches that of pentagons ABCDE and A'B'C'D'E'. Even as length of AE is not explicitly stated, we are unable to infer it based on the information in the problem.

The scale factor refers to the proportion of one figure's side length to the other figure's corresponding side length. This time, XYUV=123=4. The scaling factor is hence 4.

Each side of the pentagon A'B'C'D'E' is twice as long as the equivalent side of the pentagon ABCDE because the dilatation scale factor is 2. Therefore:

A'B' = 2AB

B'C' = 2BC

C'D' = 2CD

D'E' = 2DE

E'A' = 2EA

Segment AE, which adds up to the sum of the first pentagon's two sides, needs to be as long as possible.

AB + BC + CD + DE=AE

We can swap the value of A'B', B'C', C'D', and D'E' for AB, BC, CD, and DE, respectively, since the dilation scale factor is 2:

AE = A'B'/2 + B'C'/2 + C'D'/2 + D'E'/2

AE = (2AB)/2 + (2BC)/2 + (2CD)/2 + (2DE)/2

AB + BC + CD + DE=AE

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Answer:

2 × 2 × 3 × 7=84

Step-by-step explanation:

(a) The function sin⁻¹ has a domain of [-1, 1] and a range of [-π/2, π/2].

(b) The function cos⁻¹ has a domain of [-1, 1] and a range of [0, π].

(c) The function tan⁻¹ has a domain of (-∞, ∞) and a range of (-π/2, π/2).

In mathematics, the domain and range are concepts used to describe the inputs and outputs of a function.

The domain of a function is the set of all possible inputs or values of the independent variable for which the function is defined or meaningful.

The range of a function, on the other hand, is the set of all possible outputs or values of the dependent variable that the function can produce for all the inputs in the domain.

The inverse sine function, denoted sin⁻¹, takes as input a value between -1 and 1, and returns the angle whose sine is equal to that value. Therefore, its domain is [-1, 1], since the sine of an angle cannot exceed these limits. The range of sin⁻¹ is the set of all angles whose sine lies between -1 and 1. The smallest such angle is -π/2, which corresponds to a sine of -1, and the largest such angle is π/2, which corresponds to a sine of 1. Hence, the range of sin⁻¹ is [-π/2, π/2].

The inverse cosine function, denoted cos⁻¹, is similar to sin⁻¹, but takes as input a value between -1 and 1 and returns the angle whose cosine is equal to that value. Its domain is also [-1, 1], since the cosine of an angle cannot exceed these limits. However, the range of cos⁻¹ is different from that of sin⁻¹. It starts at 0, which corresponds to a cosine of 1, and ends at π, which corresponds to a cosine of -1. The reason for this difference is that the cosine of an angle is always positive or zero when the angle lies between 0 and π radians.

The inverse tangent function, denoted tan⁻¹, takes as input any real number and returns the angle whose tangent is equal to that number. Its domain is (-∞, ∞), since the tangent of an angle can take on any real value. The range of tan⁻¹ is between -π/2 and π/2, since the tangent of an angle becomes infinite at these values.

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Answer:

To model -2/3 + (-1 1/6) on a number line, we first need to convert the mixed number (-1 1/6) into an improper fraction.

-1 1/6 = -7/6

Now we can add -2/3 and -7/6 by finding a common denominator. The smallest common multiple of 3 and 6 is 6, so we'll convert both fractions to have a denominator of 6.

-2/3 = -4/6

-7/6 = -7/6

Now we can add them:

-4/6 + (-7/6) = -11/6

So -2/3 + (-1 1/6) = -11/6.

To model this on a number line, we would start at zero and move to the left by 1 and 2/3 units (since -2/3 is less than 1 whole unit to the left of zero). Then, we would move an additional 1 and 1/6 units to the left (since -1 1/6 is one whole unit and 1/6 of another unit to the left of zero). This would bring us to the point represented by -11/6 on the number line.

Step-by-step explanation:

Answer:

(-5/6)

Step-by-step explanation:

Start by marking the point 0 on the number line.

To represent -2/3, you'll need to move 2/3 units to the left of 0, since this value is negative. One way to do this is to divide the space between 0 and -1 into three equal parts and move two of them to the left. This brings you to the point -2/3.

To represent (-1 1/6), you'll first need to represent -1, which is one unit to the left of 0. You'll then need to add 1/6 units to the left of -1. One way to do this is to divide the space between -1 and -2 into six equal parts and move one of them to the left. This brings you to the point (-1 1/6).

To find the sum of -2/3 and (-1 1/6), you'll need to add the distances we moved in steps 2 and 3. The total distance moved to the left is 2/3 + 1/6 = 5/6. Starting from 0, we move 5/6 units to the left to arrive at the final point, which is (-5/6).

The distance between the third traffic light from the second traffic light is 35 yards.

Three traffic lights on a street span 120 yards.

If the second traffic light is 85 yards away from the first.

Therefore, the third traffic light is 120 - 85 =35 yards away from the second traffic light.

This means that the third traffic light is directly adjacent to the first traffic light. The third traffic light from the second traffic light is at the same location as the first traffic light.

Thus, the distance between the third traffic light from the second traffic light is 35 yards.

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D can be written as a single power of [tex]10: 10^{(-12).[/tex]

E. E is already a single power of [tex]10: 10^6.[/tex]

A term may be a number, a variable, the prοduct οf twο οr mοre variables, οr the prοduct οf a number and a variable. An algebraic expressiοn can cοnsist οf a single term οr a cοllectiοn οf terms. Fοr example, in the expressiοn 4x + y, the twο terms are 4x and y.

A. Since the base is the same, we can add the exponents of 10 to simplify 10(-2) * 10(-4). That is to say:

[tex]10^(-2) * 10^{(-4)} = 10^{(-2-4)} = 10^{(-6) (-6)[/tex]

As a result, A can be written as a single power of ten: 10 (-6).

B. To simplify (106 * 10(-1)) / 104 * 107, first simplify the numerator and denominator separately, then divide:

[tex](10^6 * 10^{(-1)}) / 10^4 * 10^7 = 10^{(6-1)} / 10^{(4-7)}= 10^5 / 10^{(-3)} = 10^{(5+3)} = 10^8[/tex]

As a result, B can be written as a single power of ten: 1008.

C. To simplify (104 * 107) / (103)4, we can start with the denominator:

[tex](10^4 * 10^7) / (10^3)^4 = (10^4 * 10^7) / 10^{12[/tex]

The exponents of 10 can then be added:

[tex](10^4 * 10^7) / 10^{12} = 10^{(4+7-12)} = 10^{(-1)[/tex]

As a result, C can be written as a single power of ten: 10 (-1).

D. To simplify (10(-3)),

We can multiply the exponents of 10 by 4:

[tex](10^{(-3)})^4 = 10^{(-3*4)} = 10^{(-12)[/tex]

As a result, D can be written as a single power of ten: 10 (-12).

E already has a single power of ten: 106.

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We can reduce the width of the confidence interval by increasing the sample size, reducing the confidence level and decreasing the mean (A, D, and F)

A confidence interval is an estimate of the interval that has a specified probability of including an unknown population parameter.

The purpose of a confidence interval is to estimate the true value of the population parameter being measured, such as a mean, a standard deviation, or a proportion.

In general, a wider confidence interval indicates more uncertainty about the estimate, while a narrower confidence interval suggests more precision in the estimate.

We want narrower confidence intervals to demonstrate more precision, as this allows us to draw more reliable conclusions about population parameters.

We cannot reduce the width of the confidence interval by increasing the sample size, increasing the confidence level or increasing the mean.

Thus, the correct options are a, d, and f.

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Answer:

To find the perimeter, we need to add up the lengths of all the sides. In this case, we have four sides with lengths given by the expressions 2v-5, 4v+5, 2v-5, and 8v-7.

So the perimeter P is:

P = (2v-5) + (4v+5) + (2v-5) + (8v-7)

Simplifying and combining like terms, we get:

P = 16v - 12

Therefore, the perimeter is 16v - 12.

(a)The distribution of X (the average of the 49 races) follows a normal distribution with mean 146 minutes and standard deviation 11 minutes. (b)The probability of the average of the sample being between 144 and 149 minutes is 0.5854.(c)The 80th percentile for the average of these 49 marathons is 157.2 minutes.(d) The median of the average running times is 146 minutes.

Part(a) The distribution of X (the average of the 49 races) follows a normal distribution with mean 146 minutes and standard deviation 11 minutes. Part (b) The probability that the average of the sample will be between 144 and 149 minutes in these 49 marathons can be calculated using the z-score formula: z = (x - mean)/standard deviation
For x = 144, z = (144 - 146)/11 = -0.18
For x = 149, z = (149 - 146)/11 = 0.27,using the z-score table, the probability of the average of the sample being between 144 and 149 minutes is 0.5854 (0.4026 + 0.1828).

Part (c) The 80th percentile for the average of these 49 marathons can be calculated using the z-score formula: z = (x - mean)/standard deviation, For the 80th percentile, z = 0.84 (from z-score table). Therefore, x = 146 + (0.84 * 11) = 157.2 minutes. Part (d) The median of the average running times is 146 minutes. The median is the midpoint of the data which means half of the data is above the median and half of the data is below the median. Therefore, the median of the average running times is equal to the mean.

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Answer: The numbers that cannot represent the three sides of a right triangle are {35, 84, 91}.

Step-by-step explanation: